%% Left Eigenvectors
% Create a 3-by-3 matrix.

 A = [1 7 3; 2 9 12; 5 22 7];

%
% Calculate the right eigenvectors, V, the eigenvalues, D, and the left eigenvectors, W.

[V,D,W] = eig(A)

%
% Verify that the results satisfy W'*A = D*W'.

W'*A - D*W'

% Ideally, the eigenvalue decomposition satisfies the relationship. Since eig performs the decomposition using floating-point computations, then W'*A can, at best, approach D*W'. In other words, W'*A - D*W' is close to, but not exactly, 0.
% Copyright 2012 The MathWorks, Inc.